Chapter 11.7, Problem 25P

Open-Ended Write an example of a rational function with a vertical asymptote at $x=1$ and a horizontal asymptote at $y=-5$.

To determine

To identify : the equation of the rational function

Answer to Problem 25P

The equation of the rational function is $y=\frac{1}{x-1}-5$

Explanation of Solution

Given information : The vertical asymptote at $x=1$ and a horizontal asymptote at $y=-5$

Calculation :

The graph of a rational function of the form $y=\frac{a}{x-b}+c$ has a vertical asymptote at $x=b$ and a horizontal asymptote at $y=c$

Leading $a=1$ , a possible function is

  $\begin{array}{l}y=\frac{1}{x-1}+\left(-5\right)\\ y=\frac{1}{x-1}-5\end{array}$